Home
Class 12
MATHS
Consider the function f(x)={{:((alphac...

Consider the function
`f(x)={{:((alphacosx)/(pi-2x),If,xne(pi)/(2)),(3,If,x=(pi)/(2)):}`
Which is continuous at `x=(pi)/(2)` where `alpha` is a constant.
What is `lim_(xto0) f(x)` equal to?

A

0

B

3

C

`(3)/(pi)`

D

`(6)/(pi)`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xto0)limf(x)=(alphacosx)/(pi-2x)`
`=(alpha(cos0))/(pi-2(0))=(6)/(pi)`
`:.` Option (d) is correct.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 Videos

Similar Questions

Explore conceptually related problems

Consider the function f(x)={{:((alphacosx)/(pi-2x),If,xne(pi)/(2)),(3,If,x=(pi)/(2)):} Which is continuous at x=(pi)/(2) where alpha is a constant. What is the value of alpha ?

Consider the function: f(x)={{:((alphacosx)/(pi-2x),"if "xne(pi)/(2)),(3,"if "x=(pi)/(2)):} Which is continuous at x=(pi)/(2) , where alpha is a constant. What is the value of alpha ?

Consider the function: f(x)={{:((alphacosx)/(pi-2x),"if "xne(pi)/(2)),(3,"if "x=(pi)/(2)):} Which is continuous at x=(pi)/(2) , where alpha is a constant. What is underset(xrarr0)(lim)f(x) equal to?

For what value of k, function f(x)={((k cosx)/(pi-2x)",","if "x ne (pi)/(2)),(3",", "if " x =(pi)/(2)):} is continuous at x=(pi)/(2) ?

If f(x)={{:((1-sinx)/(pi-2x),,","xne(pi)/(2)),(lambda,,","x=(pi)/(2)):},"be continuous at "x=(pi)/(2), then value of lambda is

If function f(x) given by f(x)={{:(,(sin x)^(1//(pi-2x)),xne pi//2),(,lambda,x=pi//2):} is continous at x=(pi)/(2) then lambda =

Consider the function f(x)=(sin 2x)^(tan^(2)2x), x in (pi)/(4) . The value of f((pi)/(4)) such that f is continuous at x=(pi)/(4) is

If f(x)={:{((cot x-cos x)/((pi-2x)^(3))", for " x != (pi)/(2)),(k ", for " x = pi/2):} is continuous at x= pi/2 , where , then k=

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. Consider the following functions: 1. f(x)=x^(3),x""inRR 2. f(x)=si...

    Text Solution

    |

  2. Consider the function f(x)={{:((alphacosx)/(pi-2x),If,xne(pi)/(2)),(...

    Text Solution

    |

  3. Consider the function f(x)={{:((alphacosx)/(pi-2x),If,xne(pi)/(2)),(...

    Text Solution

    |

  4. If g(x)=(1)/(f(x))andf(x)=x,xne0, then which one of the following is c...

    Text Solution

    |

  5. If f(x)=sqet(25-x^(2)), then what is Lim(x to 1) (f(x)-f(1))/(x-1) equ...

    Text Solution

    |

  6. Consider the function f(x)={{:(ax-2,"for",-2ltxlt-1),(-1,"for",-1lex...

    Text Solution

    |

  7. The function f(x)=(1-sinx+cosx)/(1+sinx+cosx) is not defined at x=pi. ...

    Text Solution

    |

  8. Consider the following functions: 1. f(x)={{:((1)/(x),if,xne0),(0,if...

    Text Solution

    |

  9. The domain of the function f(x)=(1)/(sqrt|x|-x) is

    Text Solution

    |

  10. Consider the following statements : 1. The function f(x)=x^(2)+2cosx...

    Text Solution

    |

  11. If f:IRtoIRtoIR be two functions given by f(x)=2x-3andg(x)=x^(3)+5" th...

    Text Solution

    |

  12. If f(x)=(sin(e^(x-2)-1))/(1n(x-1)), then lim(xto2)f(x) is equal to

    Text Solution

    |

  13. Consider the following statements : Statement 1 : The function f:IRt...

    Text Solution

    |

  14. Consider the function f(x)={{:(-2sinx,if,xle-(pi)/(2)),(Asinx+B,if,-...

    Text Solution

    |

  15. Consider the function f(x)={{:(-2sinx,if,xle-(pi)/(2)),(Asinx+B,if,-...

    Text Solution

    |

  16. Consider the curves f(x)=x|x|-1andg(x)={{:((3x)/(2)","xgt0),(2x","xl...

    Text Solution

    |

  17. Consider the curves f(x)=x|x|-1andg(x)={{:((3x)/(2)","xgt0),(2x","xl...

    Text Solution

    |

  18. Cosider the function f(x)=|x-1|+x^(2)" where " x""inR. Which one of ...

    Text Solution

    |

  19. Cosider the function f(x)=|x-1|+x^(2)" where " x""inR. which one of ...

    Text Solution

    |

  20. Which one the following statements is correct?

    Text Solution

    |